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Activity 1 – Set Theory and Functions for Software Engineering
Your line manager has decided that you should take on some of the company’s
development tasks. Before doing so, your line manager has collated a series of test tasks
designed to provide a comprehensive understanding of the company’s operations, focused
on tackling route planning and package sorting, to test your skills in set and graph theory
and to make sure you are ready to start working on the development of streamlining
package delivery.
Task 1
A, B, and C represent different categories of employees within the company:
● A = {employees who handle route planning}
● B = {employees who manage package sorting}
● C = {employees who oversee delivery scheduling}.
You are given the total number of employees in the company as 75 and the following data:
● the number of employees who handle both route planning and package sorting
(A ∩ B) is 10
● the number of employees who manage both package sorting and delivery scheduling
(B ∩ C) is 15
● the number of employees who oversee both delivery scheduling and route planning
(C ∩ A) is 20
● there are 8 employees who are involved in all three tasks (A ∩ B ∩ C).
Use a variety of set operations to determine the following.:
a) The number of employees who handle at least one task
b) The number of employees who handle exactly two tasks
c) The number of employees who handle only one task
d) The cardinality of each of the three categories A, B, and C.
Task 2
In computing, finding the inverse of a function can be crucial for tasks such as encryption
and decryption algorithms, where operations need to be reversed. It can also be valuable in
optimising delivery routes, where certain operations may need to be undone or traced back
to their origins.
To illustrate the importance of this concept, you are to determine the inverse of the
function, y, as given below:
= 10x2 – 4x+3
Task 3
BK Logistics deals with different categories of data and individuals daily. The
company wants to enhance its delivery operations by optimising all available resources.
Certain data sets represent different categories of resources.
Assuming and are sets of integers that can be defined as follows:
= {∣ is an even integer related to the number of route planning tasks in a day}
= {∣ is a multiple of 3, representing the number of sorted packages every three hours}.
Consider the property: =∩ = {∣ is an even integer and a multiple of 3}, indicative of
some overlapping operations between sets A and B.
Use a range of proofs (for example direct proof, proof by contradiction, proof by
contrapositive and proof by counterexample) to prove =∩.
Your line manager has decided that you should take on some of the company’s
development tasks. Before doing so, your line manager has collated a series of test tasks
designed to provide a comprehensive understanding of the company’s operations, focused
on tackling route planning and package sorting, to test your skills in set and graph theory
and to make sure you are ready to start working on the development of streamlining
package delivery.
Task 1
A, B, and C represent different categories of employees within the company:
● A = {employees who handle route planning}
● B = {employees who manage package sorting}
● C = {employees who oversee delivery scheduling}.
You are given the total number of employees in the company as 75 and the following data:
● the number of employees who handle both route planning and package sorting
(A ∩ B) is 10
● the number of employees who manage both package sorting and delivery scheduling
(B ∩ C) is 15
● the number of employees who oversee both delivery scheduling and route planning
(C ∩ A) is 20
● there are 8 employees who are involved in all three tasks (A ∩ B ∩ C).
Use a variety of set operations to determine the following.:
a) The number of employees who handle at least one task
b) The number of employees who handle exactly two tasks
c) The number of employees who handle only one task
d) The cardinality of each of the three categories A, B, and C.
Task 2
In computing, finding the inverse of a function can be crucial for tasks such as encryption
and decryption algorithms, where operations need to be reversed. It can also be valuable in
optimising delivery routes, where certain operations may need to be undone or traced back
to their origins.
To illustrate the importance of this concept, you are to determine the inverse of the
function, y, as given below:
= 10x2 – 4x+3
Task 3
BK Logistics deals with different categories of data and individuals daily. The
company wants to enhance its delivery operations by optimising all available resources.
Certain data sets represent different categories of resources.
Assuming and are sets of integers that can be defined as follows:
= {∣ is an even integer related to the number of route planning tasks in a day}
= {∣ is a multiple of 3, representing the number of sorted packages every three hours}.
Consider the property: =∩ = {∣ is an even integer and a multiple of 3}, indicative of
some overlapping operations between sets A and B.
Use a range of proofs (for example direct proof, proof by contradiction, proof by
contrapositive and proof by counterexample) to prove =∩.
